Question:
Two spheres of equal masses, one of which is a thin spherical shell and the other a solid, have the same moment of inertia about their respective diameters. The ratio of their radii will be
Two spheres of equal masses, one of which is a thin spherical shell and the other a solid, have the same moment of inertia about their respective diameters. The ratio of their radii will be
Show Hint
Thin spherical shell: \(I = \frac{2}{3}MR^2\); Solid sphere: \(I = \frac{2}{5}MR^2\).
Updated On: Apr 23, 2026
- \(5:7\)
- \(3:5\)
- \(\sqrt{3}:\sqrt{5}\)
- \(\sqrt{3}:\sqrt{7}\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Moment of inertia of thin spherical shell about diameter: \(I_s = \frac{2}{3}MR_1^2\).
Moment of inertia of solid sphere about diameter: \(I_{solid} = \frac{2}{5}MR_2^2\).
Step 2: Detailed Explanation:
Given \(I_s = I_{solid} \Rightarrow \frac{2}{3}MR_1^2 = \frac{2}{5}MR_2^2\).
\(\frac{R_1^2}{R_2^2} = \frac{2/5}{2/3} = \frac{3}{5} \Rightarrow \frac{R_1}{R_2} = \sqrt{\frac{3}{5}}\).
Thus, \(R_1 : R_2 = \sqrt{3} : \sqrt{5}\).
Step 3: Final Answer:
Thus, ratio of radii = \(\sqrt{3}:\sqrt{5}\).
Moment of inertia of thin spherical shell about diameter: \(I_s = \frac{2}{3}MR_1^2\).
Moment of inertia of solid sphere about diameter: \(I_{solid} = \frac{2}{5}MR_2^2\).
Step 2: Detailed Explanation:
Given \(I_s = I_{solid} \Rightarrow \frac{2}{3}MR_1^2 = \frac{2}{5}MR_2^2\).
\(\frac{R_1^2}{R_2^2} = \frac{2/5}{2/3} = \frac{3}{5} \Rightarrow \frac{R_1}{R_2} = \sqrt{\frac{3}{5}}\).
Thus, \(R_1 : R_2 = \sqrt{3} : \sqrt{5}\).
Step 3: Final Answer:
Thus, ratio of radii = \(\sqrt{3}:\sqrt{5}\).
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET System of Particles & Rotational Motion Questions
- The working of a rocket is based on the principle of:
- The separation between C and O-atoms in CO is 1.2 \AA. The distance of carbon atom from the centre of mass is
- Among the following, the compound that contains ionic, covalent and coordinate linkage is
- A disc of mass 5 kg and radius 50 cm rolls on the ground at 10 m/s. Find the kinetic energy.
- A particle of mass m is projected with a velocity v at an angle of \(45^\circ\) with horizontal. When the particle is at its maximum height, the magnitude of its angular momentum about the point of projection is:
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions